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    <title>czt</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>czt</b> -  chirp z-transform algorithm</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[czx]=czt(x,m,w,phi,a,theta)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>x</b>
        </tt>: input data sequence</li>
      <li>
        <tt>
          <b>m</b>
        </tt>: czt is evaluated at <tt>
          <b>m</b>
        </tt> points in z-plane</li>
      <li>
        <tt>
          <b>w</b>
        </tt>: magnitude multiplier</li>
      <li>
        <tt>
          <b>phi</b>
        </tt>: phase increment</li>
      <li>
        <tt>
          <b>a</b>
        </tt>: initial magnitude</li>
      <li>
        <tt>
          <b>theta</b>
        </tt>: initial phase</li>
      <li>
        <tt>
          <b>czx</b>
        </tt>: chirp z-transform output</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    chirp z-transform algorithm which calcultes the z-transform on a
    spiral in the z-plane at the points
    <tt>
        <b>[a*exp(j*theta)][w^kexp(j*k*phi)] </b>
      </tt> for
    <tt>
        <b>k=0,1,...,m-1</b>
      </tt>.</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

a=.7*exp(%i*%pi/6);
[ffr,bds]=xgetech(); //preserve current context
rect=[-1.2,-1.2*sqrt(2),1.2,1.2*sqrt(2)];
t=2*%pi*(0:179)/179;xsetech([0,0,0.5,1]);
plot2d(sin(t)',cos(t)',[2],"012",' ',rect)
plot2d([0 real(a)]',[0 imag(a)]',[3],"000")
xsegs([-1.0,0;1.0,0],[0,-1.0;0,1.0])
w0=.93*exp(-%i*%pi/15);w=exp(-(0:9)*log(w0));z=a*w;
zr=real(z);zi=imag(z);
plot2d(zr',zi',[5],"000")
xsetech([0.5,0,0.5,1]);
plot2d(sin(t)',cos(t)',[2],"012",' ',rect)
plot2d([0 real(a)]',[0 imag(a)]',[-1],"000")
xsegs([-1.0,0;1.0,0],[0,-1.0;0,1.0])
w0=w0/(.93*.93);w=exp(-(0:9)*log(w0));z=a*w;
zr=real(z);zi=imag(z);
plot2d(zr',zi',[5],"000")
xsetech(ffr,bds); //restore context
 
  </pre>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p>C. Bunks</p>
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